# What is Concave: Definition and 200 Discussions

In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.

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1. ### Concave mirror reflecting a point lamp, that create a wider beam

I've look if there was any way to get the "image size" or a ratio to use the Mirror Equation to find the focal length, but nothing. I think it's base on some geometry, but I don't see the relation.
2. ### Is a point of inflection concave or convex? - Which answer is correct?

but for me there is no solution to this inequality... I never wait for a ready answer but I've already spent 4 hours on it and I still don't know what to mark...
3. ### I Pentaprism with magnification, which surface is curved?

I would like to use a pentaprism with some amount of magnification. The pentaprism will be used to reflect a real image at 90 degrees angle but I also want the reflected image to appear larger. The distance between the prism and the real image is about 70cm. The pentaprism has two reflecting...
4. ### Two concave mirrors on a table

I'm currently confused in determining whether an image formed by the 1st mirror (the left one) is a real or virtual object for the 2nd mirror. Here is the solution manual: This is what I have in my mind: Since the object is located between the focus and radius point of the first mirror, the...
5. ### A Proving the Equivalence of Local and Global Maxima for Concave Functions

Consider the following theorem: Theorem: Let ##f## be a concave differentiable function and let ##g## be a concave function. Then: ##y \in argmax_{x} {f(x)+g(x)}## if and only if ##y \in argmax_{x} {f(y)+f'(y)(x-y)+g(x)}.## The intuition is that local maxima and global maxima coincide for...
6. ### Virtual and real image with concave mirror at 45 degrees

I have a spherical concave mirror with focal length of 65cm, radius of curvature of 130cm. I hold the mirror close to the eye at approximate 45 degrees and I reflect an object below it as shown in the image. The distance between the object and the mirror is 90cm, that is more than the focal...
7. ### Combination of thin lens and concave mirror

I created the following ray diagram to help me solve the problem: Then I applied the mirror equation 3 separate times. However, the final image distance I got is wrong. I'm wondering if I'm mistaken in taking the last object distance to be negative. However I only have one more try to get this...
8. ### ABCD matrix formalism for concave mirror

Hello! I need to calculate the ABCD matrix for a thick concave mirror, in the situation in which the light comes from the plane side of the mirror, and it is the concave part that is coated (for reference, I have a Fabry Perot cavity with 2 concave mirrors, and I want to mode match the laser...
9. ### Instrument using two concave lenses

Is there maybe instrument using two concave lenses? Tried to google it but found nothing. Thanks
10. ### Negative Concave Lens - Creating a Beam Expander

I am trying to create a beam expander. I purchased 3 double convex and 3 double concave lens (200mm, 300mm and 500mm). But for the diverging concave lens I need a negative -500mm lens. What exactly is a negative concave lens? I am unable to find anything on amazon or any other site that has a...
11. ### B Largest Moon With A Concave Orbit

Asimov pointed out that Earth's Moon is nowhere concave (looped) in its motion with regard to the Sun. What about Pluto and Charon - are both concave w.r.t. the Sun at certain times? Moreover, what is the largest body in the solar system which is sometimes concave w.r.t. The Sun? Thank you...
12. ### Understanding Reflection of Light on a Concave Mirror

My Basic Question is- Why can we see our inverted and real image inside a concave mirror when the image is formed in front of it and not behind? If you say that our eyes tries to image the real image formed by mirror on the mirror itself then- Imagine a situation where we have a concave mirror...
13. ### Can you make a more focused beam by using convex and concave lens?

When you put a convex and then concave lens in front of a light source, the light will be parallel but narrower than when it came in such as in a laser beam expander/compressor. Using a pen laser and a convex and concave lens, is it possible to focus the beam by putting a convex then a concave...

15. ### Solving for intervals of concave up and concave down

Is this correct?
16. ### Correct statement about a concave mirror

Option (a) is wrong because if the person is standing at the focal point of the mirror, no image will be produced Option (b) is wrong because concave mirror can produce magnified image Option (c) is wrong because concave mirror can produce upright image Option (d) is wrong because sharp image...
17. ### MHB 4.2.251 AP calculus exam concave ?

ok this one baffled me a little but isn't $g = e^{-t^2}$and the graph of that has an inflection point at x=1
18. ### A What does the concave multifractal spectrum shape physically mean?

I investigate the damage to the metal surface with box-counting method and some surface images give a convex multifractal spectrum f for a result - which is also widespread in the literature, but some other surface images form a concave multifractal spectrum. Not much information is available on...
19. ### Can a convex reflection be corrected using a concave mirror?

If one took a photograph of a reflection from convex reflective surface. Could one use concave mirror to obtain the original undistorted image?
20. ### How we see image inside the concave mirror when object is beyond C?

In concave mirror, when object is beyond C ( centre of curvature) our traditional Ray diagrams show a real and inverted image formed between C and F. But at the same time, if we look directly into the mirror and remove the screen, we see an inverted image which appears to be inside the mirror...
21. ### Proof involving convex function and concave function

Homework Statement [/B] Let X be a vector space over ##\mathbb{R}## and ## f: X \rightarrow \mathbb{R} ## be a convex function and ##g: X \rightarrow \mathbb{R}## be a concave function. Show: The set {##x \in X: f(x) \leq g(x)##} is convex. Homework Equations [/B] If f is convex...
22. ### I Paddle convex and concave sides and forward propulsion

Hello everyone, In stand up paddle boarding, the correct way to use the paddle when moving forward is to have the paddle convex side facing rearward while the paddle pushes water backward. This is explained by the fact that the paddle generates a lift force pointing backward if the convex side...
23. ### About a concave mirror with a large focal length (1000mm)

I have a Cassini PM-160 spherical mirror used in telescopes as the primary mirror. The mirror is concave with a radius of curvature of 2600mm and focal length of 1300mm. I have a very basic question. If an on object is located beyond the focal length of a concave mirror then the virtual image...
24. ### Location of object on axis of concave mirror?

Homework Statement Where on the axis of a concave mirror would you place an object to get a half-size image? Express the object distance in terms of the focal length f. Follow the sign convention. Homework Equations (1/q)+(1/p)=(1/f) f=(2/R) The Attempt at a Solution I attempted to use the...
25. U

### Do Concave Mirrors Always Form Real Images?

i want to know the concave mirros is always real images or any difference then how to calculate thanks and regards Uday
26. ### Apply Fermat's principle to a Concave mirror

I am now taking optics class at my school. Fermat principle can be applied on mirror of course. Then what about Concave mirror? According to the calculus of variation. the optimized path(actual path of the light) should be the shortest path. but in the concave mirror case, it goes through the...
27. ### Algebraic Explanation of Image Formation in Convex Lenses

Homework Statement An object is in the focal length of a convex lens. As the object is moved from the focus towards the lens, what happens to the object? Homework Equations 1/f=1/d0+1/di The Attempt at a Solution I know how to solve this problem using ray diagrams, and the solution is: The...
28. ### MHB Can Discontinuity and Non-Derivability Exist in Strongly Concave Functions?

Hey! :o Could you give me an example of a strong concave function $f:[0,3]\rightarrow \mathbb{R}$ that is not continuous? (Wondering) We have that $f''(x)<0$. Since the function has not to be continuous, the derivatives are neither continuous, are they? (Wondering) Is maybe the...
29. ### Imaging by cylindrical concave mirror

Consider an upright cylindrical concave mirror with a point source located at the focal point of the mirror. By upright I mean that the mirror is plane in the vertical direction and a concavity in the horizontal plane. Now it seems likely that you would see a virtual image of the point source...
30. ### MHB What is a concave function and how is it determined?

I was reading some where that $\sqrt{x}$ is concave function what does it mean.
31. ### Finding focal point of concave lens using concave and convex

Homework Statement [/B] I was doing http://stao.ca/VLresources/sci-tie-data/lessons/1400_1499/DivergingLensExperimentDeta.pdf experiment. Let's look at this image: Suppose we get the imaginary object at dv by convergence lens. And this object is like a real object for the concave lens. Then...
32. ### Why do convex lenses magnify, and why don't concave lenses?

So knowing that convex lenses causes light to converge and concave lenses causes then to diverge, why does converging light create a larger image than diverging light? Magnification means we want to see more of a certain part of an object, meaning we want to enlarge that section and have it...
33. ### Image Distance with two concave lenses

Homework Statement An object 1.25 cm tall is placed 100 cm in front of a convex lens with a focal length of magnitude 50 cm. A concave lens with a focal length of magnitude 20 cm is placed 90 cm beyond the first lens. Where is the final image located? Homework Equations (1/s)+(1/s')=1/f s=...
34. ### Concave mirror: Reflected rays do not meet at one point

I have drawn a diagram of the incident and reflected rays of an object by the concave mirror. Red color shows the incident rays, black color shows the normals drawn from the center of curvature, while green color shows the reflected rays. Shouldn't all the reflected rays meet at one point. Any...
35. ### Help with lenses for hand-made telescope

I'm trying to make a handmade telescope, but I'm stuck with the lenses I bought 2 lenses. they are the same "convex from one side and concave from the other side" like glasses lenses. then I knew that I need a double convex for both the object lens and the eyepiece lens. so I decided to put the...
36. ### How to solve for distance of object with a concave mirror?

Homework Statement An object is placed a distance do in front of a concave mirror with a radius of curvature r = 6 cm. The image formed has a magnification of M = 4.3. Solve for the object's distance. Homework Equations M = -di/do (1/do) + (1/di) = 2/R = 1/f The Attempt at a Solution I've tried...
37. ### Ball rolls without sliding in a concave bowl

Homework Statement Ball of mass m and radius r rolls without sliding in a bowl of radius R. Express it's angular velocity ω as a function of the angle θ. What are the normal force and friction force as a function of θ. Homework Equations Moment of inertia of a solid ball round it's center...
38. ### Position of Final Image in Concave Mirror with Glass Block

Homework Statement A glass block of thickness 60 cm and refractive index 4/3 is placed in front of a concave mirror. A light source is then placed on the center of curvature of the concave mirror. Find the position of the final image formed. (Focal length is 30 cm) Homework Equations...
39. ### MHB Graph Sketching (concave)

Hello again :) I am doing a question in which I have to find the mistake that is in one of these points and must change one of these criteria to make it correct. So first I am drawing a graph to get an outline of what it looks like. -f(x) is defined on (−∞, ∞) and differentiable twice through...
40. ### MHB Concave Up or Down? Identifying Inflection Points in a Polynomial Function

Determine the intervals on which $$y=3x^5 - 5x^4 - 60x^3 + 80$$ $$y'=15{x}^{4}-20{x}^{3}-180{x}^{2}$$ $$y''=60{x}^{3}-60{x}^{2}-360x$$ $$y''\left(0\right)=-2,0,3$$ Is concave up or concave down, identity inflection points. Mutiple choiceA. The function is concave up on___ and concave down...
41. ### Effect of a distant cold object in focus of concave mirro.

Pictets 1790 experiment shows the apparent reflection of cold from ice in the focus of a concave mirror onto an air thermometer held in the focus of a second concave mirror 12 feet away. As soon as the screen shielding the 'cold' concave mirror is moved aside the distant thermometer in the...
42. ### Why does the two concave mirror illusion looks realistic wh

while a simple concave mirror projection does not?Hi, I'm really not sure where does this question go, but perhaps this is as good a place as any... If not, then I would appreciate a referring to the right place. So, I have encountered this nifty, decades old, illusion created by combining two...
43. ### Image formed from object at focal point of concave mirror

The question posed: "An object is located to the right of a mirror that in concave in its [the object's] direction. If the object sits on the focal point of the mirror, what answer best describes the image formed?" Our class is united in the notion that as the rays would be parallel...
44. ### Image formed by a plane-concave lens and a concave mirror

Homework Statement An observer looks at an object of height 2 cm through a plane-convex lens of radius 20 cm and refraction index 1.5. There's a concave mirror of radius 30 cm 40 cm behind it, and the object is at the same distance of both the lens and the mirror. Find the images formed by the...
45. ### MHB What Are the Properties of Concave/Convex Spherical Mirrors?

Spherical mirrors. We are given p= +18 and the mirror is concave with f= 12. Find r, i, m, Real or Virtual, Imaginary or not imaginary, and what side of the mirror is the image on. All units are cm. r: f=r/2, so r=2f r= 24 cm i: (1/p) + (1/i)= (1/f), so (1/f)-(1/p)=(1/i) i= 36 cm m...
46. ### Create DIY Light Intensifier Using Disposable Materials

1. I am supposed to create a device that can intensify the light directed at a light intensity sensor. A small light bulb will be 25 cm away from the light sensor. My device is required to be 20cm long and placed in between the light bulb and the light sensor in order to make the light that is...
47. ### Fourier optics with concave (diverging) lenses

Hey, I was wondering, since for a convex lens the Fourier transform of a fields is in their real focus plane. Is it for a concave lens that the Fourier transform of a field is in the virtual focus plane? I can't find any book or paper that talks about how concave lenses work in terms of...
48. ### Refraction through a glass slab + reflection off a concave mirror

Homework Statement An object is placed 21 cm in front of a concave mirror of radius of curvature of 10 cm. A glass slab of thickness 3 cm and RI =1.5; is then placed close to the mirror. Find the position of the final image. Take distance of closer side of block as 1 cm from the mirror...
49. ### How to Obtain a Magnification of -2 from a Convex Lens?

Homework Statement You wish to obtain a magnification of -2 from a convex lens of focal length f. The only possible solution is to: A) place a virtual object at a distance 2f/3 from the lens. B) place a virtual object at a distance 5f/3 from the lens. C) place a real object at a distance...
50. ### Diverging and Converging lenses in a system

Homework Statement A)Find the final position of the image (from the object, I assume?) B)Find the size of the final image of the object. Homework Equations 1/f = 1/do + 1/di The Attempt at a Solution 1) Solved first distance: 1/5 - 1/4 = 1/di --> 4/20 - 5/20, di = -20cm 2) Use di1 for do...